Questions tagged [kerr-metric]

The Kerr metric describes the geometry of empty spacetime around a rotating uncharged axially-symmetric black hole.

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What happens if $ a^2 > M^2 $ in Kerr metric?

(Boyer-Lindquist coordinates and $ c = G =1 $ taken) As I know, line element in Kerr metric $ d s^2 = - \left( 1 - \frac{2Mr}{\rho^2} \right) d t^2 - \frac{4 M a r \sin^2 \theta}{\rho^2} d \phi d t + \...
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Is it possible that black holes spin in discreet spin quanta?

Roy Kerr recently wrote a paper critical of the Penrose singularity theorem. One interpretation of his paper is that the singularity problem might be an artifact of the Schwarzchild metric and that a ...
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The Kerr metric applied to a solid rotating body

Can the Kerr metric be used as an exterior solution to analyse the vacuum outside a rotating solid body or does it only apply to a rotating black hole? If it can't, is there an alternative exterior ...
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Calculating the determinant of the Kerr metric

I have been trying to calculate the determinant of the Kerr metric (described by equation 11.71, A First Course in General Relativity: 3rd Edition, B. Schutz): $$\begin{align}ds^2 &=-\frac{(\Delta-...
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Finding the Four-Velocity vector in the Kerr spacetime between two points?

For over a year me and a friend have been working on a Kerr Black Hole renderer. We are close to the finish line and get renders like these; These renders show aberration of light due to the cameras ...
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Causality violation in Kerr metric

my professor told me that in Kerr metric, there is a zone of causality violation around the ring singularity, but he was saying this in the context of $M^2>a^2$, does this also apply to the cases ...
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Question on the transformation from Boyer-Lindquist to Kerr-Schild coordinates, for a modified Kerr metric

From Kerr metric, we do know that there exist a function with the form of: $$\Delta = r^2 - 2 M r + a^2 \tag{1}.$$ Following $[1]$, I did understand the coordinate transformation from Boyer-Lindquist (...
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Hawking radiation from photons?

I am reading a lot of papers that derive the Hawking temperature solving either the Klein Gordon equation for scalar fields or the Dirac equation for spin $\tfrac12$ particles via tunnelling ...
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Question about Kerr's recent paper regarding Penrose et al.'s works on gravitational singularities [duplicate]

R. Kerr posted an essay on arxiv recently. Kerr claims: The consensus view for sixty years has been that all black holes have singularities. There is no direct proof of this, only the papers by ...
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Is it possible for an object on an initially retrograde orbit to pass through the ergosphere or a rotating black hole and emerge?

I say "initially retrograde" because am aware that while inside the ergosphere, everything necessarily has prograde motion. So the two options I can envision are: The object approaches the ...
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What metric can describe best the spacetime outside a rotating star?

I hope this question is not mistreated as a duplicate, because that is not my intention. The Kerr metric suffices to describe the exterior solution to an axisymmetric spacetime mass distribution of ...
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Asymptotic development of the black-hole metric

In the Kruskal-Szekeres extension of the Schwarzschild metric parallel universes appear. In a couple of questions on this site, for instance: Where does the parallel universe in the Penrose diagram ...
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Why does Roy Kerr claim that the Kerr black hole does not contain a singularity?

In a preprint posted on the arXiv, Roy Kerr claims that there is a widespread misunderstanding related to the singularity inside the black hole that bears his name. Can anyone explain his argument in ...
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Redshift near Kerr Black Hole

The question is related to Sean Carroll's Spacetime and Geometry ex 6.6. Consider a Kerr black hole with an accretion disk of negligible mass. Particles in the disk follow geodesics. Some iron in the ...
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Schwarzschild and Kerr solution in $(x, y, z, t)$ coordinates?

The Schwarzschild solution ('simple' black holes) and the Kerr solution (rotating black holes) are very well known in General Relativity. The coordinates which are used to describe them are mostly ...
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Rotating Black Holes and Birkhoff's theorem

I found a few questions that are similar to mine, but I do not think that either of them answers exactly what I want: Is there a Birkhoff-like theorem for stationary axisymmetric metrics? or ...
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Coordinate transform of Kerr metric to Kerr-Schild coordinates

the transformation from Boyer-Lindquist $\{t,r,\theta,\phi\}$ coordinates to Kerr-Schild $\{t',r,\theta,\phi' \}$coordinates can be written as $$ dt' = dt + \frac{2 M r}{r^2 - 2 M r + a^2} dr, \;\;\; ...
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How to describe the four-current of a tilted loop in Kerr spacetime

consider the Kerr metric in Boyer-Lindquist coordinates. We usually describe the source of an electromagnetic field by the four vector $J^\mu$. $$J^\mu = \{\rho, j^1, j^2, j^3\}.$$ Now we have an ...
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Is there a distance at which the Kerr metric looks like the Schwarzschild metric?

As the title says: Is there a distance at which the Kerr metric looks like Schwarzschild metric? Edit: if there isn't any such distance (smaller than infinity), can we measure from the outside, with ...
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Spheroidal eigenvalues with shifted boundary conditions

I was studying the spheroidal differential equation in relation to calculating solutions for fields in a general Kerr background metric and, as far as I can tell, the eigenvalues $\lambda$ that enter ...
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What vacuum should be defined for a observer in Kerr spacetime?

A scalar field in Kerr spacetime can have two kinds of modes, one labeled by "in", and the other by "up". The "in" modes originate from the past null infinity, while the &...
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Carter Constant with a Cosmological Constant

The Carter constant for the Kerr Newman metric $$ \rm C = p_{\theta}^{2} + \cos^{2}\theta \ \Bigg[ a^2 \ (m^2 - E^2) + \left(\frac{L_z}{\sin\theta} \right)^{2} \Bigg] $$ with (in $[+---]$ signature) $$...
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What are the effects on a stationary observer at a specific distance from a Kerr Black Hole?

A Kerr Black Hole (BH) is a spinning BH. There is an Event Horizon (EH) which is $$r_H^\pm =\frac{r_{S} \pm \sqrt{r_{S}^2 - 4a^2}}{2},$$ where $a = \frac{J}{Mc}$ and $r_{S}$ is the Schwarzschild ...
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Physical meaning of Boyer-Lindquist coordinate

The Kerr metric in the Boyer-Linquist coordinate is $$\mathrm{d} s^{2}= \frac{\Delta}{R^{2}}\left(\mathrm{d} t-a \sin ^{2} \theta\, \mathrm{d} \phi\right)^{2}-\frac{\sin ^{2} \theta}{R^{2}}\left[\...
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Spacetime metrics extended to negative radius

In the Kerr metric $$ ds^2=\left(1-\frac{2Mr}{\rho^2}\right)dt^2+\frac{4Mar\sin^2\theta}{\rho^2}dtd\varphi-\frac{\rho^2}{\Delta}dr^2-\rho^2d\theta^2-\left(r^2+a^2+\frac{2Ma^2r\sin^2\theta}{\rho^2}\...
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What would Hawking radiation look like from inside the event horizon?

Let’s say you fell into a rotating black hole, the inner horizon of the black hole is an infinite blue shift surface, so you should be able to observe events from the arbitrarily far future before ...
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Why are there two interior regions in this diagram?

Why are there two interior regions in this diagram? There seems to be two inner horizons, and two wormhole regions. Where do the two such regions comes from? What determines which reason someone falls ...
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Where do the other black holes in this diagram come from?

In this Penrose diagram for a charged/Rotating black hole, once your in the new universe you can continue onward to an infinite sequence of black holes/white holes. So I'm asking, where do those black ...
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Blandford-Znajek process - energy flow reverse and other questions

In the original BZ paper [1] from 1977, the authors invoke a number of facts and conclusions that I do not quite follow. In the hope that someone has read it and was able to grasp all the details, I ...
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What happens when two ergospheres of oppositely spinning black holes of the same mass, axis of rotation, and angular momentum approach?

What happens when two ergospheres of oppositely spinning black holes of the same mass, axis of rotation, and angular momentum approach each other? What would happen to the black holes in question?
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How can I make the Kerr black hole surfaces scale well in my diagrams?

I've read that the equatorial radius of the ergosphere of a rotating black hole is the Schwarzschild radius. But in this animation made in natural units by Yukterez it doesn't apply. I then used ...
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Could a Star orbit a rotating black hole inside the ergosphere? If so, how big should the black hole be? [duplicate]

Could a Star orbit a rotating black hole inside the ergosphere? If so, how big should the black hole be? I imagine it should be absolutely massive so that tidal forces are minimal. And if all this is ...
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A question about Kerr black holes and Hawking radiation

It's a common myth that somoene falling into a black hole will see the entire history of the universe before they cross the event horizon. With a Kerr black hole however, it's sort of true. The inner ...
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The angular momentum of zero mass limit of Kerr metric

The Kerr metric in Boyer coordinates is $$ ds^2 = -\left(1 - \frac{2GMr}{r^2+a^2\cos^2(\theta)}\right) dt^2 + \left(\frac{r^2+a^2\cos^2(\theta)}{r^2-2GMr+a^2}\right) dr^2 + \left(r^2+a^2\...
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Dropping a spinning top into a black hole?

Is there a formal treatment for what happens when one drops a spinning top into a black hole? More precisely, if one has a spinning top, of mass $m$ and angular momentum $j$, and lets it drop into a ...
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What are the correct equations for the frequency of a photon along kerr geodesics?

As a photon orbits close around a Kerr black hole in an elliptical orbit that reaches into its ergosphere, the frequency of the light ray should increase due to frame-dragging. Given that: $$ v = f \...
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What Would An Arbitrarily Close Shell Observer See in a Kerr Black Hole?

In a Schwarzschild Black hole an arbitrarily close shell observer (near the event horizon) would see any object falling in asymptotically approach the speed of light. Is there any point w/i Kerr ...
Tak Robin's user avatar
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The Papapetrou transformation. Conditions to be satisfied to achieve requirements of transformation

I'm looking at the Papapetrou transformation in Ch. 6, $\S 52$ of Chandrasekhar's book. He cf's Ch. 2, $\S$11. I understand Ch. 2, $\S$11. There he considers a coordinate transformation, \begin{align*}...
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How to plot spherical geodesics in the Kerr metric in maple?

I need to plot geodesics in the Kerr Newman Nut metric, but to do that I need to understand how to build geodesics for an already known Kerr metric in maple. I understand that in order to build ...
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Wave operator in Kerr spacetime: change of coordinates

The wave equation for a scalar field, in Kerr geometry and in Boyer-Lindquist coordinates, reads: $$-\left[\frac{(r^2 + a^2)^2 }{\Delta} - a^2 \sin^2\theta \right] \partial^2_t \Phi - \frac{4Mar}{\...
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Orbital period around slowly rotating star in general relativity

I want to compute the general relativity prediction for the difference in period between clockwise and countercloskwise orbits of a planet around a star which has small mass $M$ and small angular ...
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Energy Flux Through Horizon

In Kerr spacetime, given the energy-momentum tensor $T^{ab}$ of a field, what is the energy flux (as measured at infinity) $$ \frac{d^2E}{dt d\Omega} $$ i.e., the amount of energy passing through the ...
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Interference pattern of scalar wave around a Kerr black-hole

If a scalar field is scattered around a Kerr black-hole, its amplitude will be amplified, keeping the frequency of the wave constant. So consider two waves; one is coming out from the horizon $(r_* \...
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Super-radiant amplification in electromagnetic perturbation in Kerr background

Let an electromagnetic field be scattered by a Kerr black-hole; then its amplitude will be amplified, but its frequency will remain same (super-radiant amplification). Hence though its intensity will ...
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What is spinning in a spinning black hole? [duplicate]

When a rotating star collapses into a neutron star, the resulting object spins at a huge number of rpm due to its much smaller volume and the conservation of angular momentum. What happens when a ...
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Fundamental gravitational wave frequency for Kerr black holes?

Just as the usual rotating pulsars (neutron stars) have fundamental frequency(ies) tied to the rotational frequency, does it happen in Kerr black holes too? What are the frequencies of rotating Kerr ...
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How are Black Holes shadow and deviation from circularity measured? [closed]

After the images of M87* and SgrA* black holes from the EHT collaboration, Black Hole Physics have entered in a new "astrophysical" era. I've started to read about these objects recently, ...
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Variational formulation for the Kerr solution

The critical points of the Einstein-Hilbert action, if one allows axial symmetry, are Kerr-type solutions of the Einstein field equations, in which a parameter $\alpha$ interpreted as the angular ...
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How does one covert from Cartesian coordinates to Boyer-Lindquist coordinates?

I am new to physics stackexchange, but I have a question which I seem to have not been able to find an answer to. I already know that the transformations from Boyer-Lindquist coordinates to Cartesian ...
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Principle null congruences of Kerr metric

I am trying to derive the principle null congruences of Kerr metric in Boyer-Lindquist coordinate, which is $$t=r+\left( m+\frac{m^2}{(m^2-a^2)^{\frac{1}{2}}}\right)ln|r-r_+|+\left( m-\frac{m^2}{(m^2-...
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